Face-on structure of barlenses and boxy bars: an insight from spectral dynamics.

Based on the spectral analysis of individual orbits of stars from different $N$-body models, we show that the face-on morphology of the so-called `face-on peanut' bars (boxy bars) and barlenses is supported by different families of orbits. For `face-on peanut' bars, the family of boxy orbits comes to the fore, and it is responsible for the unusual morphology of the bar in the central regions. In the models with compact bulges, the bars show a barlens morphology in their central parts. We found that the barlens supporting orbits come in two types, one of which gives a square-like shape and the other have a rosette-like shape in the frame co-rotating with the bar. Such a shape is typical for orbits moving in simple spherical potentials. Both these types of orbits do not precess together with typical bar orbits. Square-shaped orbits were already known from some of the previous studies, while the second orbital type is revealed for the first time in the present work. Although quite simple, the family of rosette-like orbits is found to be the main building block of a barlens in our models. The detailed analysis of all bar orbits also allowed us to distinguish x2 orbital family and isolate the structure supported by its orbits. The x2 family is well-known, but, apparently, for the first time in studies of this kind, we have fully revealed its supported structure. We found that x2 family population increases with an increase in central matter concentration.